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The table shows the growth, in centimeters, of plants in two different soils after two weeks.

Soil Type vs. Plant Growth

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Soil A & 3.1 & 5.2 & 4.6 & 3.8 & 6.0 & 4.3 & 3.7 & 4.0 & 3.5 & 3.5 \\
\hline
Soil B & 2.9 & 3.8 & 5.0 & 4.8 & 4.5 & 3.9 & 3.9 & 4.4 & 5.5 & 4.1 \\
\hline
\end{tabular}

Which statement explains which soil tended to have greater growth?

A. Soil A had greater growth because its data have a greater standard deviation.
B. Soil A had greater growth because its data have a greater mean.
C. Soil B had greater growth because its data have a greater interquartile range.
D. Soil B had greater growth because its data have a greater median.

Sagot :

GinnyAnsweridn
Let's analyze the growth data for plants in soils A and B to determine which soil tended to have greater growth.

First, we calculate the mean growth for each soil type:
- Mean growth for Soil A: [tex]\(4.17\)[/tex] cm
- Mean growth for Soil B: [tex]\(4.28\)[/tex] cm

Next, we calculate the standard deviation for each soil type, which measures the variation or dispersion of the growth data:
- Standard deviation for Soil A: [tex]\(0.8391\)[/tex] cm
- Standard deviation for Soil B: [tex]\(0.6925\)[/tex] cm

We also calculate the median growth for each soil type, which is the middle value when the data points are ordered:
- Median growth for Soil A: [tex]\(3.9\)[/tex] cm
- Median growth for Soil B: [tex]\(4.25\)[/tex] cm

Finally, we calculate the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile, providing a measure of statistical dispersion:
- IQR for Soil A: [tex]\(0.975\)[/tex] cm
- IQR for Soil B: [tex]\(0.825\)[/tex] cm

Now, we assess the given statements:

1. "Soil A had greater growth because its data have a greater standard deviation."
- This statement is not accurate since standard deviation alone does not determine greater growth; it only indicates variability in the data.

2. "Soil A had greater growth because its data have a greater mean."
- This statement is incorrect because the mean growth for Soil A ([tex]\(4.17\)[/tex] cm) is actually less than that for Soil B ([tex]\(4.28\)[/tex] cm).

3. "Soil B had greater growth because its data have a greater interquartile range."
- This statement is incorrect because Soil B has a smaller IQR ([tex]\(0.825\)[/tex] cm) compared to Soil A ([tex]\(0.975\)[/tex] cm).

4. "Soil B had greater growth because its data have a greater median."
- This statement is correct because the median growth for Soil B ([tex]\(4.25\)[/tex] cm) is greater than the median growth for Soil A ([tex]\(3.9\)[/tex] cm).

Therefore, the correct statement is:
Soil B had greater growth because its data have a greater median.
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